Emily is 32 years older than Daniel. Nine years ago, Emily was 5 times as old as Daniel. How old is Daniel now?
Answer: We can use the given information to write down two equations that describe the ages of Emily and Daniel. Let Emily's current age be $e$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $e = d + 32$ Nine years ago, Emily was $e - 9$ years old, and Daniel was $d - 9$ years old. The information in the second sentence can be expressed in the following equation: $e - 9 = 5(d - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $e$ and substitute it into our second equation. Our first equation is: $e = d + 32$ . Substituting this into our second equation, we get the equation: $(d + 32)$ $-$ $9 = 5(d - 9)$ which combines the information about $d$ from both of our original equations. Simplifying both sides of this equation, we get: $d + 23 = 5 d - 45$ Solving for $d$ , we get: $4 d = 68$ $d = 17$.